Alligation or Mixture problems
- 1. The concentration of glucose in three different mixtures (glucose and alcohol) is 12,35 and 45 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. What is the ratio of glucose and alcohol in the new mixture?
Options- A. 3:2
- B. 4:3
- C. 2:3
- D. 3:4 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 3:2
Explanation:
Concentration of glucose are in the ratio =
Quantity of glucose taken from A = 1 liter out of 2
Quantity of glucose taken from B = 3/5 x 3 = 1.5 lit
Quantity of glucose taken from C = 0.8 lit
So, total quantity of glucose taken from A,B and C = 3.6 lit
So, quantity of alcohol = (2 + 3 + 1) - 3.6 = 2.4 lit
Ratio of glucose to alcohol = 3.6/2.4 = 3:2
- 2. One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.
Options- A. 27 %
- B. 26 %
- C. 29 %
- D. 21 % Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO, Network Engineer, Project Manager
Correct Answer: 27 %
Explanation:
Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135
X = 27
So, required percentage of benzene = 27 %
- 3. Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?
Options- A. 193 : 122
- B. 97 : 102
- C. 115 : 201
- D. 147 : 185 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 193 : 122
Explanation:
Given the three mixtures ratio as (1:2),(2:3),(3:4)
(1+2),(2+3),(3+4)
Total content = 3,5,7
Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105
105/3 = 35 , 105/5 = 21 , 105/7 = 15
Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)
i.e (35,70), (42,63), (45,60)
So overall mixture ratio of milk and water is
35+42+45 : 70+63+60
122:193
But in the question asked the ratio of water to milk = 193 : 122
- 4. The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
Options- A. 8:3
- B. 6:7
- C. 7:5
- D. 11:7 Also asked in: CAT, Bank Exams, AIEEE, Bank PO
Correct Answer: 7:5
Explanation:
Milk in 1-litre mixture of A = 4/7 litre.
Milk in 1-litre mixture of B = 2/5 litre.
Milk in 1-litre mixture of C = 1/2 litre.
By rule of alligation we have required ratio X:Y
X : Y
4/7 2/5
\ /
(Mean ratio)
(1/2)
/ \
(1/2 ? 2/5) : (4/7 ? 1/2)
1/10 1/1 4
So Required ratio = X : Y = 1/10 : 1/14 = 7:5
- 5. An alloy of copper and bronze weight 50g. It contains 80% Copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?
Options- A. 45 gm
- B. 50 gm
- C. 55 gm
- D. 60 gm Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 50 gm
Explanation:
Initial quantity of copper = = 40 g
And that of Bronze = 50 - 40 = 10 g
Let 'p' gm of copper is added to the mixture
=> = 40 + p
=> 45 + 0.9p = 40 + p
=> p = 50 g
Hence, 50 gms of copper is added to the mixture, so that the copper is increased to 90%.
- 6. In what ratio must wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg so that the mixture be worth Rs. 3/kg?
Options- A. 1:2
- B. 3:2
- C. 2:1
- D. 2:3 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 2:1
Explanation:
Given rate of wheat at cheap = Rs. 2.90/kg
Rate of wheat at cost = Rs. 3.20/kg
Mixture rate = Rs. 3/kg
Ratio of mixture =
2.90 3.20
3
(3.20 - 3 = 0.20) (3 - 2.90 = 0.10)
0.20 : 0.10 = 2:1
Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.
- 7. A milkman has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk. If the cost of pure milk is Rs. 18 per litre, then the profit of the milkman, when he sells all the mixture at cost price, the profit % ?
Options- A. 22.5%
- B. 25%
- C. 20%
- D. 33.33% Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 25%
Explanation:
As water costs free, water sold at cost price of milk gives the profit.
Required profit % = 5/20 x 100 = 5 x 5 = 25%.
- 8. There are two mixtures of honey and water in which the ratio of honey and water are as 1:3 and 3:1 respectively. Two litres are drawn from first mixture and 3 litres from second mixture, are mixed to form another mixture. What is the ratio of honey and water in it ?
Options- A. 111:108
- B. 11:9
- C. 103:72
- D. None Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 11:9
Explanation:
From the given data,
The part of honey in the first mixture = 1/4
The part of honey in the second mixture = 3/4
Let the part of honey in the third mixture = x
Then,
1/4 3/4
x
(3/4)-x x-(1/4)
Given from mixtures 1 & 2 the ratio of mixture taken out is 2 : 3
=>
=> Solving we get the part of honey in the third mixture as 11/20
=> the remaining part of the mixture is water = 9/20
Hence, the ratio of the mixture of honey and water in the third mixture is 11 : 9 .
- 9. In what ratio must a merchant mix two varieties of oils worth Rs. 60/kg and Rs. 65/kg, so that by selling the mixture at Rs. 68.20/kg, he may gain 10% ?
Options- A. 2:3
- B. 4:3
- C. 3:4
- D. 3:2 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 3:2
Explanation:
Let he mixes the oils in the ratio = x : y
Then, the cost price of the oils = 60x + 65y
Given selling price = Rs. 68.20
=> Selling price = 68.20(x+y)
Given profit = 10% = SP - CP
=> 10/100 (60x + 65y) = 68.20(x+y)-(60x + 65y)
=> 6x + 6.5y = 8.20x + 3.20y
=>2.2x = 3.3y
=> x : y = 3 : 2
- 10. In a mixture of 240 lt. water is 20% and rest is Milk. What quantity of mixture should be taken out and replaced with water so that water becomes 40%?
Options- A. 60 lit
- B. 55 lit
- C. 45 lit
- D. 50 lit Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 60 lit
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